My background in math is through differential equations, and I have used statistics over much of my life and I have a math question I need help with.

There is a correlation between C02 and world Temperature. What is it? For instance, 100 ppm of C02 = 3 Degrees Celsius

What is the correlation coefficient for the correlation? (.7 and up is considered a good correlation)

How was causation established?

Your help would be appreciated.

There is no direct correlation between X amount of CO2 and X increase in temperature because of the nature of how GHGs work. The solar output is relatively stable, but relatively is not absolutely stable. There are also other factors which can come into play that impact the temperature outside of the solar output and the energy retained by the GHGs. The discussion into the temperture impact of increasing GHGs goes back to the late 1800s.